Check the following, look in the "Lightroom sub-folder" (see screen shot) and if there is a file ending in .lock, delete this file and then try and restart Lightroom.

When Lightroom is open it places this file next to the opened catalog to ensure that it is not possible for any other user to access the catalog. If Lightroom shuts down unexpectedly the file remains in place and prevents Lightroom from opening. This file is temprory and is deleted when Lightroom is closed normally.